UV stretching when subdividing - how to avoid
A simpler example to see what is happening here:



Now we add a loop cut on the conic part:



And if the loop cuts were on the cylinder part:



In both cases, the proportions are respected in the mesh point of view. But the vertices which are displaced by the subsurface modifier are not at the same position in the UV map. So, they are not kept in place (relatively) the same way.

... a bit hard to explain... but I hope this example is enough to get the point.

In your model, cuts are mainly on the equivalent of the cylinder part here, plus, some are in the cylinder part and others in the conic part (the seam is mixed). So you have distortions.